Theorems · Definition · category theory

CategoryTheory.IsFiltered.sup

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.IsFiltered C] →
      (O : Finset C) → Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y)) → C

An arbitrary choice of object "to the right" of a finite collection of objects O and morphisms H, making all the triangles commute.

Defined in: Mathlib.CategoryTheory.Filtered.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsFiltered

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
Finsetstatement and proof · cited by 13,712
CategoryTheory.IsFilteredstatement and proof · cited by 210
CategoryTheory.IsFiltered.sup_existsproof · cited by 5

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.IsFiltered.toSupstatement · cited by 4
CategoryTheory.IsFiltered.toSup_commutesstatement · cited by 1
CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisorproof · cited by 0
CategoryTheory.IsFiltered.toSup.congr_simpstatement · cited by 0
CategoryTheory.Limits.colimitLimitToLimitColimit_surjectiveproof · cited by 0